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The first open channel for yield-stress fluids in porous media

Published online by Cambridge University Press:  03 February 2021

Dimitrios Fraggedakis Open the ORCID record for Dimitrios Fraggedakis [Opens in a new window] ,
Emad Chaparian Open the ORCID record for Emad Chaparian [Opens in a new window]  and
Outi Tammisola Open the ORCID record for Outi Tammisola [Opens in a new window]
Dimitrios Fraggedakis*
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA02139, USA
Emad Chaparian
Affiliation:
Mathematics Department, University of British Columbia, Vancouver, BCV6T 1Z2, Canada
Outi Tammisola
Affiliation:
Linné FLOW centre, Department of Engineering Mechanics, KTH Royal Institute of Technology, SE-10044Stockholm, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

The prediction of the first fluidized path of yield-stress fluids in complex porous media is a challenging yet important task to understand the fundamentals of fluid flow in several industrial and biological processes. In most cases, the conditions that open this first path are known either through experiments or expensive computations. Here, we present a simple network model to predict the first open channel for a yield-stress fluid in a porous medium. For porous media made of non-overlapping discs, we find that the pressure drop ${\rm \Delta} P_c$ required to open the first channel for a given yield stress $\tau _y$ depends on both the relative discs size $R_s$ to the macroscopic length $L$ of the system and the packing fraction $\phi$. The non-dimensional pressure gradient ${\rm \Delta} P_c R_s/ \tau _y L$ (i.e. the critical yield number), however, depends on the packing fraction $\phi$ only, leading to a mastercurve for all examined ratios of $R_s/L$. In the case of non-overlapping discs, we find ${\rm \Delta} P_c R_s/ \tau _y L\sim \phi /(1-\phi )$. We also report the statistics on the arclength of the first open path. Finally, we discuss the implication of our results for the design of porous media used in energy storage applications.

JFM classification

Low-Reynolds-number flows: Porous media Non-Newtonian Flows: Plastic materials
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A58
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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